photo and dark current mechanisms in …qj736sk9775/thesis shanbin...photo and dark current...

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PHOTO AND DARK CURRENT MECHANISMS

IN ORGANIC HETEROJUNCTION SOLAR CELLS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Shanbin Zhao

March 2010

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/qj736sk9775

2010 by Zhao Shanbin. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

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http://creativecommons.org/licenses/by-nc/3.0/us/http://creativecommons.org/licenses/by-nc/3.0/us/http://purl.stanford.edu/qj736sk9775

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Peter Peumans, Primary Adviser


Mark Brongersma


Michael McGehee

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

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Copyright by Shanbin Zhao, 2010.

All Rights Reserved.

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Abstract

Organic photovoltaic (OPV) cells can potentially become the renewable energy

source of choice because of their advantages such as flexibility and low-cost. Over

the past decade, extensive research attention has focused on increasing the power

conversion efficiency of OPV cells with record efficiencies near 6%, still falling far

short of the efficiency achieved in traditional inorganic solar cells. Further

improvements in OPV cell performance will require a thorough understanding of the

physical processes that govern photocurrent generation.

It is usually assumed that non-geminate recombination is the most important

loss mechanism that can be minimized by increasing the carrier mobilities. We have

modeled the separation of the geminate charge-pair at a donor-acceptor interface of

arbitrary geometry using kinetic Monte Carlo simulations. We find that the geminate

carrier recombination process that takes place at the donor-acceptor immediately

following exciton dissociation determines the shape of the photocurrent-voltage

characteristics and contributes significantly to losses in organic donor-acceptor solar

cells. The ratio of the electron mobility in the acceptor material over the hole

mobility of the donor material (or vice versa), and not the absolute carrier mobility,

determines the geminate separation probability and fill factor. These results are

confirmed by intensity, voltage, intentional doping, and temperature dependent

photocurrent measurements on planar and bulk heterojunctions.

Abstract

v

We performed capacitance-voltage measurements on simple bilayer organic

solar cells as a function of temperature. These measurements provide information

about the electrically active doping concentration and the ionization energy of these

dopants. Band structures were calculated for the doping density and ionization

energy typically found for various temperatures, and Monte Carlo simulations of the

geminate pair separation process were performed, providing a complete model for

photocurrent generation that matches experimental observations closely.

The Shockley diode equation has been used extensively to explain the dark

current in donor-acceptor organic heterojunctions, but without thorough justification.

We show experimentally that these devices cannot be modeled accurately using

Shockleys model. The fit to Shockleys diode equation is coincidental and holds for a

single temperature only. A new model was proposed and shown to fit experimental

data.

The work provides precise guidelines for increasing the efficiency of organic

heterojunction photovoltaic cells.

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Acknowledgement

I would like to express my appreciation to many individuals and organizations who

have contributed to this work.

It is a great honor for me being a member of Professor Peter Peumans research

group. For the past five years, his profound insight, creative spirit and remarkable

enthusiasm have led to numerous enlightening conversations, which opened up so

many pathways during the hardest times. Meanwhile, the great flexibility he offered

has allowed me to extensively explore the massive resources provided by the

university, which made my graduate life an invaluable experience.

I would like to thank Professor Michael D. McGehee for all the knowledge he

gave me in his series of classes, necessary for performing the research in this work.

My interest in organic electronics originated from his class, dated back to the first

quarter I arrived on campus, and during the years I have taken four classes with him,

all quite relevant to my research area. The collaboration with professor McGehees

group is also an essential part of this work.

I would like to thank Professor Mark L. Brongersma, who lectured the first

semiconductor physics class in my graduate life. His unique method of conveying the

physical concepts with body motions is indeed impressive.

Acknowledgement

vii

I would like to thank Professor Zhenan Bao, who chaired the defense committee.

The questions she brought up with her deep knowledge of organic electronics in

general have helped to make the work more precise and accurate.

I would like to thank Professor Baylor Triplett, who has contributed numerous

hours helping me out on the ESR machine. His detailed explanations, including

examples and references have given me great help.

I would like to thank all the group members in our research group, Uraib Aboudi,

Mukul Agrawal, Rostam Dinyari, Serena Faruque, Whitney Gaynor, Kevin Huang, Jong

Yon Kim, Kyunglok Kim, Jung-Yong Lee, Albert Liu, Joy Liu, Xavier Martinet, Olivier

Pincon, Seung-Bum Rim, Nicholas Sergeant, Himanshu Verma, Trudie Wang, Junbo

Wu. It is a great fortune to join such a group of young talented colleagues. We used

to occupy the whole CISX 213 office space, and for every single second in that room, I

was either talking to someone else, or listening to someone elses talking, which

provided both the hardest critics and most constructive opinions to my work.

Some of the projects reflect the joint effort from other individuals or groups,

including BASF, IMEC, and Professor Thompsons group at USC, especially Doctor

Barry P. Rand from IMEC, who contributed both experimentally and theoretically to

this work.

The Stanford Nanofabrication Facility staffs have provided many helps, either by

giving me the training on some of the tools, or taking care of the CISX building related

issues, they are James Conway, Jeannie Perez, Marie Peterson, Mary Tang, Uli

Thumser, and David Cala.

Acknowledgement

viii

Administrative issues have been taken care of by Trish Halloran-Krokel, Fi

Verplanke, Stephanie Sorensen, Doris Chan, Billie Kader, so that I can focus more on

the research side of my graduate life.

Outside the eight hours every day, during which I was supposed to be working in

the lab, I was with my friends, who made the past six years so enjoyable and full of

memorable moments.

I would also express my appreciation to Annette Isaacson and Paul Heft, who

hosted me for the first three nights when I first arrived in the states. We have

become friends since then, and the sharing of bitterness and happiness of life has

meant so much to me.

My family members were all at the other side of the Pacific Ocean, for the whole

duration of my graduate study, however, that does not stop them showing their

constant love and support, without which, I would not imagine finishing this work.

For that reason, I am greatly indebted to all of them.

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Table of Contents

Abstract ............................................................................................... iv

Acknowledgement ............................................................................... vi

List of Tables ........................................................................................ xi

List of Figures ...................................................................................... xii

1 Introduction .................................................................................... 1

1.1 Organic semiconducting materials ............................................................... 1

1.1.1 Small molecular semiconductors .................................................. 2

1.1.2 Polymeric semiconducting materials ............................................ 4

1.2 Advantage and disadvantage of organic materials ...................................... 6

1.3 Bibliography .................................................................................................. 8

2 Geminate separation ....................................................................... 9

2.1 Photocurrent generation .............................................................................. 9

2.2 Geminate vs. non-geminate recombination .............................................. 11

2.3 Modeling geminate recombination ............................................................ 15

2.4 Comparison with experimental data .......................................................... 18

2.5 Bibliography ................................................................................................ 20

3 Doping in donor acceptor heterojunctions .................................... 22

3.1 Electric field insufficiency by intrinsic material .......................................... 22

3.2 Doping enhanced electric field ................................................................... 25

3.2.1 Unintentional doping in organic materials .................................. 26

3.2.2 Example of organic dopants ........................................................ 28

3.2.3 Capacitance voltage measurement ............................................. 29

3.3 Temperature dependent ionization ........................................................... 30

3.3.1 Experiment details ....................................................................... 30

3.3.2 Temperature dependent exciton diffusion ................................. 32

3.3.3 Temperature activated ionization ............................................... 34

3.4 Temperature impact on geminate separation ........................................... 40

3.4.1 Langiven Capture Radius ............................................................. 41

3.4.2 Isolating the ionization effect ...................................................... 41

3.5 Bibliography ................................................................................................ 43

4 Geminate separation in bulk heterojunctions................................ 45

Table of contents x

x

4.1 Motivation for BHJs .................................................................................... 45

4.1.1 Bulk heterojunctions ................................................................... 46

4.1.2 Tandem cells ................................................................................ 48

4.1.3 Light trapping cells ....................................................................... 48

4.2 Simulation of BHJ structure ........................................................................ 49

4.3 Sensitivity analysis ...................................................................................... 52

4.3.1 Thickness dependence ................................................................ 53

4.3.2 Mobility ratio dependence .......................................................... 55

4.3.3 Grain size dependence ................................................................ 59

4.4 Bibliography ................................................................................................ 60

5 Multicarrier model ........................................................................ 61

5.1 Introduction ................................................................................................ 62

5.2 Structures of devices .................................................................................. 63

5.3 Modeling particle behavior ........................................................................ 65

5.3.1 Kinetic Monte Carlo ..................................................................... 66

5.3.2 Stabilization ................................................................................. 67

5.4 Mobility combination optimization ............................................................ 69

5.5 Sub-linear photocurrent vs. light intensity ................................................. 71

5.6 Intrinsic recombination rate ....................................................................... 72

5.7 Energetic disorder ...................................................................................... 73

5.8 Bibliography ................................................................................................ 76

6 Dark current mechanism ............................................................... 78

6.1 Open circuit voltage limited by dark current ............................................. 79

6.2 Traditional view on dark current mechanism ............................................ 80

6.3 Interface recombination ............................................................................. 83

6.3.1 Exponential tail of DOS ................................................................ 84

6.3.2 Activation energy ......................................................................... 87

6.3.3 Interfacial recombination model ................................................. 89

6.4 Open circuit voltage explanation ............................................................... 90

6.5 Bibliography ................................................................................................ 93

7 Conclusion and Future work .......................................................... 96

7.1 Purification and impurity identification techniques .................................. 97

7.2 Interface studies ......................................................................................... 98

7.2.1 Engineering the LUMO/HOMO levels ......................................... 98

7.2.2 Further exploration of recombination mechanism ..................... 99

7.2.3 Metal/organic junction ................................................................ 99

7.3 Tandem solar cells .................................................................................... 100

7.4 Full device numerical model ..................................................................... 101

7.5 Bibliography .............................................................................................. 102

xi

List of Tables

Table 2.1 Values of physical parameters implemented in the simulation ................... 17

Table 3.1 Values of physical parameters implemented in the simulation ................... 39

Table 5.1 Parameters for kinetic Monte Carlo ............................................................. 65

Table 6.1 Activation energy extracted from experimental data, for 6 device structures.

Measure voltage is different in order to maximized the usage of the log linear regime

data on current density vs. voltage characteristics, across different temperatures. .. 89

xii

List of Figures

Figure 1.1: Chemical structures of four small molecules. (a) copper phthalocyanine

(CuPc), (b)C60, (c) 3,4,9,10-perylene tetracarboxylic bis-benizimidazole (PTCBI),

(d)Pentacene (Pc). .......................................................................................................... 3

Figure 1.2: Chemical structures of polymers. (a) poly[2-methoxy-5-(2'-ethyl-

hexyloxy)-1,4-phenylene vinylene] (MEH-PPV), (b) poly 3-hexylthiophene (P3HT). ..... 5

Figure 2.1 Schematic of photocurrent generation process. ........................................ 10

Figure 2.2 Geminate recombination vs. non-geminate recombination ...................... 12

Figure 2.3 Schematic of relation between current density and light intensity, for

geminate and non-geminate dominated recombination mechanisms ....................... 13

Figure 2.4 Current density vs light intensity data from Ref. [6]. CuPc/PTCBI bulk

heterojunction. The two curves show relations at two different applied voltages.

Insets: band diagram for two applied voltage conditions. ........................................... 14

Figure 2.5 ExperimentalI I~V curves (curves) of three various CuPc/PTCBI devices

fitted by simulation results (open dots). Solid (planar), dashed (disordered BHJ) and

dotted (ordered BHJ) experimental curves are from Ref. [10], [6] and [11],

respectively. The disordered BHJ was fitted using the 4.04 nm branch diameter

simulated BHJ. The ordered BHJ data was simulated using an interpenetrating square

pillar geometry with a checker-board arrangement of 40 nm wide pillars. All three

model geometries have an 80 nm thick active region. The BHJ models assume a BHJ

region that is 60 nm thick. For all three curves, mobility ratio = 0.01 is applied. All the

BHJ related terms will be explained in later chapters. ................................................. 19

Figure 3.1 Band diagram and photocurrent generation in intrinsic bilayer DA

heterojunctions. ........................................................................................................... 23

Figure 3.2 Theoretical result for GEHP dissociation probability vs applied field, in

bilayer cells, top curve. Onsager model is plotted in the bottom curve, for comparison

purpose only. ................................................................................................................ 24

Figure 3.3 Comparison of the band diagram of intrinsic material vs. that of doped

materials, with field across the interface calculated for typical doping conditions .... 25

Figure 3.4 Left: Experimental I~V curve of CuPc/BPE-PTCDI(unpurified), (squares)

freshly made, (triangles) four hour air exposure. Lines are fittings with model in the

work. Right: Short-circuit condition band-diagram with doping level indicated. ........ 27

List of figures xiii

xiii

Figure 3.5 Doping mechanism of F4-TCNQ as n-type dopant for zinc phthalocyanine

(ZnPc) and N,N-diphenyl-N,N-bis(1-naphthyl)-1,1-biphenyl-4,4-diamine (-NPD).

Figure taken from Ref [6]. ............................................................................................ 28

Figure 3.6 Photocurrent vs voltage, for four different temperatures. ITO/40nm

CuPc/40nm PTCBI/100nmAg. Same cell, with all conditions kept the same, except the

temperature. ................................................................................................................ 31

Figure 3.7 (a) LD as a function of temperature, as calculated with Eeff = 80meV. (b)

Experimental photocurrent measured at -1V, scaled by a single factor (open circles),

fitted by calculated exciton diffusion efficiency, with same parameters as in (a)....... 34

Figure 3.8 Capacitance voltage measurement, plotted as 1/C2 vs Voltage, for 200K,

250K, 300K, respectively. Open triangle: experimental data. Dotted line: theoretical

fittings. .......................................................................................................................... 35

Figure 3.9 Solid cureves: Ionization for 4x1017/cm3 doping, 0.27eV doping level,

measured from the corresponding LUMO/HOMO. Squares: experimentally measured

ionization level. Plus sign: measured ionization from the calculated curve. The insets

are schematics of the ionization of dopants ................................................................ 36

Figure 3.10 Calculated band structure under short circuit condition, for (a) 300K, (b)

250K, (c) 200K, (d) 150K, with ionization values shown in figure 3 (b). Solid lines are

LUMO and HOMO levels, dotted lines are Fermi levels. .............................................. 38

Figure 3.11 Solid curves: Photocurrent vs voltage, for four different temperatures.

ITO/40nm CuPc/40nm PTCBI/100nmAg. Same cell, with all conditions kept the same,

except the temperature. Open squares: simulated photocurrent. ............................. 40

Figure 3.12 IQE vs. voltage, simulated with geminate separation model, with

ionization profile fixed for all temperatures. ............................................................... 42

Figure 4.1 Bilayer DA photovoltaic cell structure. Light absorption length and exciton

collection region thickness are shown. Exciton collection region is marked with yellow

band. ............................................................................................................................. 46

Figure 4.2 The three methods that tackle the trade-off between long absorption

length and short exciton diffusion length. On the right hand side, from top to bottom,

they are BHJ, tandem cell, and light trapping. ............................................................. 47

Figure 4.3 Schematic of cellular automata method. This is only cross-section view of

the 3-D simulation. (a) Before exchange, (b) after exchange. ..................................... 50

Figure 4.4 Example structure generated by cellular automata method.

ITO/CuPc/CuPc:PTCBI/PTCBI/Ag, transparent region is PTCBI, blue region is CuPc. ... 52

Figure 4.5 Cross-sectional view of BHJ devices. ITO /CuPC /CuPc:PTCBI /PTCBI /Ag.

Total thickness of the active region is 80nm for both devices. Thickness of the BHJ

region (t) are different, (a) t=10nm, (b) t=60nm. ......................................................... 53

List of figures xiv

xiv

Figure 4.6 Thickness dependence of IQE vs. Voltage curves. The physical parameters

remain the same as in Table 2.1, except the thickness of the mixing region.

Concentration of CuPc vs. PTCBI is 1:1, measured by volume. Mobility of electrons

and holes are the same. ............................................................................................... 55

Figure 4.7 Thickness dependence of IQE vs. Voltage curves. The physical parameters

remain the same as in Table 2.1, except the thickness of the mixing region.

Concentration of CuPc vs. PTCBI is 1:1, measured by volume. Mobility h=1000e. .. 56

Figure 4.8 (a) Cross-section of the simulated BHJ with 10.3 nm branch diameter

(periodic boundary conditions apply). (b) PD as a function of position along the DA

interface, for MR=1. The diameter of the dots is proportional to PD for a GEHP

generated at that point. The open dot is a reference, with a diameter equivalent to

100%. (c) Same as (b) except MR=100. ........................................................................ 57

Figure 4.9 (a) IQE as a function of charge carrier mobility ratio MR. The BHJs have 60

nm thick junction regions, with branch diameters of 10.3 nm (squares) and 4.04 nm

(circles) respectively. Markers are simulated data for 0 V (solid symbols) and 0.4 V

(open symbols) applied voltage, and the lines are a guide to the eye. Results for a

planar cell are shown for comparison (triangles)......................................................... 58

Figure 5.1 Different heterojunction structure used for simulations in this chapter.

Each column is a single device, with the upper part the geometry of acceptor, and the

bottom part the donor. Gray materials are the electrodes. (a)&(e) BHJ with 9nm grain

size, (b)&(f) BHJ with 4nm grain size, (c)&(g) ordered structure with 10nm by 10nm

square cross section for each phase, (d)&(h) planar junction. BHJs are generated with

cellular automata method explained in previous chapters. ........................................ 64

Figure 5.2 Stabilization of simulations. The number of electrons and holes are

recorded when new photo absorption event happens. The thick vertical line indicates

the threshold after which information is summarized to calculate the characteristics

such as IV, concentration profile, etc. .......................................................................... 68

Figure 5.3 Internal quantum efficiency and geminate recombination fraction as a

function of mobilities combination for different geometries. Each column is a device,

with the upper part the IQE, and the bottom part the GRF. (a)&(e) BHJ with 9nm

grain size, (b)&(f) BHJ with 4nm grain size, (c)&(g) ordered structure with 10nm by

10nm square cross section for each phase, (d)&(h) planar junction. BHJs are

generated with cellular automata method explained in previous chapters. ............... 70

Figure 5.4 Current density and geminate recombination fraction vs. light intensity

curves. For BHJ with 9nm grain size. Mobility value is 10-5cm2/Vs for both charge

carriers. ......................................................................................................................... 71

Figure 5.5 Internal quantum efficiency vs. intrinsic recombination rate R, for different

mobility combinations, 10nm grain size BHJs. ............................................................. 73

List of figures xv

xv

Figure 5.6 IQE~Voltage curves for BHJs and planar cells. (a) & (b) 9 nm branch BHJs. (c)

& (d) Planar cells. We appy Guassian disorder model, and the standard deviation is

shown meV. .................................................................................................................. 74

Figure 6.1 Schematic of photocurrent component (dotted black curve), darkcurrent

component and total output current, for various devices. The photocurrent is

idealized to be voltage independent, and the only difference in the three devices is

the dark current and hence total output current. ....................................................... 79

Figure 6.2 Current density vs. voltage characteristics at different temperatures. (a)

Calculated for ideality factor n=1.5. (b) ITO /CuPc(40) /PTCBI(40) /Ag(100), dotted

lines are fits to Eq 2, and calculated ideality factor is noted beside the lines.

Thicknesses are given in nm. (c) ITO /CuPc(20) /C70(32.5) /BCP(10) /Ag(100) (d) ITO

/Pentacene(55) /C60(50) /BCP(10) /Ag(100) ............................................................... 81

Figure 6.3 (a) Schematic band diagram for dark current mechanism, solid arrow

indicates recombination, dotted arrow indicates diffusion current over the barrier. (b)

Schematic for recombination event, when CT state and exciton formation involved,

where one or both recombination particles need to be thermally activated. ............ 84

Figure 6.4 (a) Schematic of DOS in amorphous organic solids. Calculated using

Gaussian center with 50meV standard deviation, cut off at 50meV, and followed by

exponential tail. (b) Exponential tail of LUMO filled with electrons according to Fermi-

Dirac distribution. (c) Number of charge carrier changes due to Fermi level change. (d)

Number of charge carrier changes little due to temperature change. ........................ 85

Figure 6.5 Calculated alpha value, for different Fermi level, for a exponential DOS,

with characteristic length 40meV. Numbers in the legend refers to Fermi level,

negative means below the center of the double sided exponential distribution.

Squares are values that matches CuPc/PTCBI dark IV. ................................................ 86

Figure 6.6 Current density vs. temperature, for different systems at fixed voltages

listed in Table 1, straight lines are fits according to Equation 6.2. .............................. 88

Figure 6.7 (a)&(b) Voc vs temperature, under 51 mW/cm2 and 160 mW/cm2

illumination. Solid triangles are experimental data, and open triangles are calculated

value. (c)&(d) Voc vs Illumination Intensity, at 225K and 250K. .................................. 92

1

Chapter 1

1 Introduction

In this chapter we will give some background explanation necessary for the

understanding of the whole thesis. The first part is a general overview of organic

semiconductor materials used as the building block for organic photovoltaic (OPV)

devices, with a focus on small molecules. The second part will contribute to some

device structure analysis, their advantages and disadvantages.

1.1 Organic semiconducting materials

The word organic has been historically related to biological material, which has come

from a once-living organism and has the capability of decay. With the development

of organic synthesis industry, millions of organic compounds can be made in

laboratories and fabrication facilities, many of which do not exist naturally at all.

Since the middle of last century, people start to discover the electrical properties of

certain organic compounds, specifically, the semiconducting property [1]. Hence the

understanding of these materials has grown in parallel to that of inorganic materials,

such as silicon. Different types of organic electronic devices has been made as well,

Chapter 1. Introduction 2

including organic thin film transistors (OTFT) [2] [3] [4], organic light emitting diodes

(OLEDs) [5] , and organic photovoltaics [6].

The distinct feature of organic semiconductor, compared with inorganic

counterparties, is that within a single molecule, atoms are covalently bonded, while

between molecules, van der Waal force dominants, if not serves as the only bonding

force. Hence the electronic coupling within a single molecule is quite strong, which is

not the case for inter-molecule range. One of the most important reasons that OLED

has been a successfully industrialized product lies in the fact that organic

semiconductors typically has strong optical-electrical coupling, compared with

inorganic counterparties, due to the strong localized electron orbitals, hence a

higher internal/external quantum efficiency (IQE/EQE) can be achieved.

Organic semiconducting materials can be categorized into two groups: small

molecular semiconductors vs. polymeric semiconductors.

1.1.1 Small molecular semiconductors

As can be conceived from the name, this group of materials typically carries a small

amount of atoms within each single molecule, with the number ranging from several

to a couple hundred. Historically, small molecular materials has been the origin of

study for organic semiconducting properties, together with the optical properties,

including gas, liquid and solid phase.

Figure 1.1 shows the chemical structures of four widely used small molecular

materials, with molecular weights far below 1000. A common feature that can be


observed at first sight is the highly conjugated structure. The bonding can be seen

all through the backbone of the structures, which is an indication that the electronic

orbital is highly hybridized across the whole molecule, which intuitively makes the

transportation of electrons, or holes, through the molecule possible.

Figure 1.1: Chemical structures of four small molecules. (a) copper

phthalocyanine (CuPc), (b)C60, (c) 3,4,9,10-perylene tetracarboxylic bis-

benizimidazole (PTCBI), (d)Pentacene (Pc).

One of the great advantage of small molecules is the easy processing technique

required for organizing them into a working device. As the molecular weight is small,

these materials are readily sublimable, which makes them fascinating candidate for


vapor phase deposition, the same technique that has been used for various

industries for over a hundred years. Besides, the vapor phase deposition has minimal

effect on the underlying structure during the fabrication process of a device, which

makes them good candidates for multilayered or even more complicated devices.

These can been seen when compared with larger molecules as polymer based ones.

1.1.2 Polymeric semiconducting materials

Parallel to small molecular semiconducting materials, there is another huge

population of organic semiconductors, which bears the name polymers. Polymers are

large molecules composed of repeating structural units connected by covalent bonds.

Due to the extraordinary range of properties accessible in polymeric materials, they

have traditionally played an essential and ubiquitous role in everyday life - from

plastics and elastomers on the one hand to natural biopolymers such as DNA and

proteins that are essential for life on the other. Compared with these applications,

the history of polymers being used as semiconducting device building blocks is

relatively short. For tens of years people have studied the optical-electronic

properties of them and have come to the conclusion that certain polymers are

excellent materials for optical-electronic applications, due to their mechanical,

optical, electrical and chemical properties.

Figure 1.2 shows the typical polymers that have been used for OLEDs and OPVs.

Similar with small molecule case, the whole backbone of the polymer is connected


with conjugated bonds, hence making the transportation of electrons and holes

along the backbone fairly easy.

Figure 1.2: Chemical structures of polymers. (a) poly[2-methoxy-5-(2'-ethyl-

hexyloxy)-1,4-phenylene vinylene] (MEH-PPV), (b) poly 3-hexylthiophene

(P3HT).

As has been explained above, backbone is main part where optical-electronic

property originates, while side chains bear the function of modification of physical

properties, including changing the band gap, and the solubility. The direct

consequence is two advantages. First of all, absorption/emission spectrum can be

easily changed due to the modification of the side chains, which is also called

functional groups. Secondly, by attaching alkyl chains with reasonable length, the

whole polymer chain can be dissolved in organic solvents, and this is something of

standard procedure nowadays in polymer design. Once being dissolved in solutions, a


whole spectrum of solution based processing techniques can be used, including but

not limited to, drop casting, spin casting and ink jet printing, or even screen printing.

1.2 Advantage and disadvantage of organic materials

One natural question often raised in public is, why so much effort is thrown into the

development of organic electronics, especially at the historical stage when inorganic

semiconductors has been studied for so many years, with matured products being

used all around the world. The question is certainly non-trivial, and if it is, either of

the following has already happened: Organic has taken up the whole market, or, it is

a finished and proven to fail technology.

As is true for all unresolved debates, there are pros and cons for this new

material category as well. Firstly, we can talk about the advantages that are unique to

organics. Cost is an essential part that determines the survival of a technology in

todays world. In this arena, organic certainly has its unique advantage. It does not

require high impurity, as compared to inorganics. Device performance does depend

on purity levels, with high purity levels preferred for better performances [7],

however, the impurity level tolerance of organic is much higher. Part of the reason is

due to the highly localized orbitals, which translate into shorter infection range of

impurity molecules/atoms. Processing techniques have be listed in previous sections,

all of which are low cost compared with silicon and germanium. In addition to that,


large area electronics can be achieved fairly easily with evaporation or solution based

processed.

There are advantages unrelated to cost as well. As flexible as organic materials

are, they can be printed onto flexible substrates. This is directly related to the

technique being used at places where flexible substrates are required. The properties,

including electrical, optical or even chemical/physical ones, can be tuned. For

example, by adding functional groups to cyclometalated platinum complexes, the

emission spectra can be tuned within the visible range, from red to blue [8].

Certain disadvantages do exist. Top of the list is the difficulty for structural

control. State of the art OTFTs are small molecular single crystals, with extremely

high projected production cost, due to the low yield and long growth time.

Extensively studies organic systems are all amorphous systems, where precise

structural control is a touch away from impossibility. Although precise control is not

required, it does show up to be the bottleneck from the transfer of lab-generated

patents to fab-made products. The understanding of the structure dependent optical

electronic properties is still an active research area.


1.3 Bibliography

[1] Pope M. and Swenberg C.E., Electronic Processes in Organic Crystals. Oxford:

Oxford University Press, 1982,

[2] Ebisawa, "ELECTRICAL PROPERTIES OF POLYACETYLENE/POLYSILOXANE

INTERFACE." J. Appl. Phys., vol. 54, pp. 3255, 1983.

[3] Tsumura, "Macromolecular electronic device: field-effect transistor with a

polythiophene thin film," Appl. Phys. Lett., vol. 49, pp. 1210, 1986.

[4] D. Mascaro and , "Forming oriented organic crystals from amorphous thin

films on patterned substrates via solvent-vapor annealing," Organic Electronics, vol.

6, pp. 211, 2005.

[5] TANG, "ORGANIC ELECTROLUMINESCENT DIODES," Appl. Phys. Lett., vol. 51,

pp. 913, 1987.

[6] TANG, "2-LAYER ORGANIC PHOTOVOLTAIC CELL," Appl. Phys. Lett., vol. 48,

pp. 183, 1986.

[7] Forrest, "Ultrathin organic films grown by organic molecular beam deposition

and related techniques," Chem. Rev., vol. 97, pp. 1793, 1997.

[8] Brooks, "Synthesis and characterization of phosphorescent cyclometalated

platinum complexes," Inorg. Chem., vol. 41, pp. 3055, 2002.

Chapter 2

2 Geminate separation

In this chapter we will introduce the basic physics of photocurrent generation

process in organic donor acceptor (DA) heterojunction (HJ) solar cells, with a focus on

geminate separation and recombination. Modeling of the processes with Monte

Carlo is described, and the results are analyzed in detail.

2.1 Photocurrent generation

A DA solar cell typically contains the following four major components: (I) a

transparent electrode on top of glass as the bottom electrical contact, such as

indium-tin-oxide (ITO), (II) an electron donor material, (III) an electron acceptor

material, and (IV) a metallic top contact, such as silver. A schematic is shown in Figure

2.1 The highest occupied molecular orbital (HOMO) and lowest unoccupied

molecular orbital (LUMO) of the donor materials sit above those of the acceptor

material, for the following reason: in organic semiconductors, the binding energy for

exciton is normally high, on the order of 1 eV [1] [2], and hence thermally splitting

the exciton into electron hole pairs is a process with very small rate, compared to

exciton decay. Therefore with a single active light absorption layer, most photo

excited excitons decay and contribute no photocurrent. To overcome this obstacle,

Chapter 2. Geminate separation 10

energy offset on the HOMO and LUMO helps the charge transfer (CT) process

happens energetically favorably.

Figure 2.1 Schematic of photocurrent generation process.

As shown in Figure 2.1, the conversion of optical into electrical energy occurs in

four consecutive steps[2, 3]. First, photon absorption leads to a Frenkel exciton

generation. Separation of this exciton into free electrons and holes is unlikely

because of the large exciton binding energies we have explained. In a second step,

excitons diffuse via energy transfer processes [1] over a diffusion length (LD). In a

third step, those excitons that reach the DA interface rapidly dissociate into an

electron in the acceptor and a hole in the donor via an ultrafast charge transfer (CT)

process [4], leading to a Coulombically bounded geminate electron-hole pair (GEHP)

across the DA interface [5]. In a fourth step, the GEHP can subsequently be separated

by an electric field at the DA interface, followed by collection of the electron and hole


at cathode and anode, respectively, where the remaining electrochemical potential is

used to drive an external load [2].

There is quantum efficiency associated with each subprocess, and the total

external quantum efficiency (EQE) can be expressed as:

= EQE A ED CT CC (2.1)

where A represents the absorption efficiency, ED represents the exciton diffusion

efficiency, CT represents the charge transfer efficiency, and CC represents the

charge collection efficiency. Another gauge of the conversion efficiency is internal

quantum efficiency (IQE), which is defined in the following way:

= EQE ED CT CC (2.2)

2.2 Geminate vs. non-geminate recombination

A major loss mechanism for planar cell structures that appears in IQE is the

recombination of electrons and holes at the interface, immediately following CT

process. The recombination can happen in two ways, as shown in Figure 2.2. If the

recombining electron and hole originates from the same exciton, it is called a

geminate recombination, while on the other hand, if they originate from different

excitons, it is called a non-geminate recombination. Clearly, geminate recombination

is a uni-molecular process and the recombination probability is independent on the

carrier concentrations. Non-geminate recombination is a bimolecular process, and


hence the recombination probability is sensitive to carrier concentration, it typically

increases as carrier concentration goes up. As understanding the recombination

becomes a critical task for the optimization of solar cell conversion efficiency, we

naturally have the question, which of the above two mechanism dominates, and how

do we reduce recombination in each case.

Figure 2.2 Geminate recombination vs. non-geminate recombination

As we look closely into the mathematically representation of photo generated

current, we get the following relationship:

2

Generation RecombinationJ R R

J L n n

(2.3)


where J is the photocurrent density, RGeneration and RRecombination are the generation and

recombination of GEHPs, L is the light intensity, n is the electron concentration, , ,

and are constants. The intuition is that, photo current density is proportional to

carrier density within the device, and there are two extinction terms, with the linear

term coming from geminate, and the non-linear term coming from the non-geminate

recombination. Therefore, the difference between the dependence of photocurrent

density on light intensity is clear, if the non-geminate recombination dominates, we

should see sublinear behavior, and if geminate recombination dominates, we should

see linear relationship, as shown in Figure 2.3.

Figure 2.3 Schematic of relation between current density and light intensity,

for geminate and non-geminate dominated recombination mechanisms

With the theoretical bases formed in the previous paragraph, we now look into

experimental data for evidence. Figure 2.4 shows the current density vs. light

intensity plots, for CuPc/PTCBI bulk heterojunctions (BHJs), which will be analyzed in

detail in later chapters. For short circuit condition, a linear relation prevails, which is


a clear sign that geminate recombination dominates. This is not so surprising, if we

look into the inset band diagram, for short circuit condition, the built-in voltage drops

linearly across the whole device, and the driving force is quite large to separation the

charges, which means the accumulation of charges is quite hard. Now if we inspect

the 0.4 V applied voltage plot, we can see that the curve is still strictly linear. This is

strong supportive evidence for geminate dominant recombination, as now the

separation force for the charges is quite small, due to the flattened band diagram.

Figure 2.4 Current density vs light intensity data from Ref. [6]. CuPc/PTCBI

bulk heterojunction. The two curves show relations at two different applied

voltages. Insets: band diagram for two applied voltage conditions.


2.3 Modeling geminate recombination

Now we know that the geminate separation is the dominant mechanism, an in-depth

study of this process is helpful for the minimization and improve the efficiency of

solar cells. The GEHP dissociation probability (PD) in the bulk of a material under a

uniform electric field was derived by Onsage in 1938 [7]. PD depends on the balance

between Coulomb attraction and an electric field of external or built-in origin. At

planar DA heterojunctions, electron and hole diffusion is constrained by the DA

interface leading to an enhancement in PD. It was concluded that the electric field

dependence of PD governs the current-voltage characteristics of such planar devices

[3]. The modeling of the constrained diffusion process is non-trivial and we used

Monte Carlo method for the task.

To model the geminate charge separation and recombination process, we

include four successive sub-processes[3]: (1) exciton diffusion over a diffusion length

= /6, where d is the lattice constant, is the intrinsic exciton hopping rate, and is the exciton lifetime, (2) exciton dissociation into a GEHP upon reaching the

DA interface, (3) electron and hole hopping within the acceptor and donor materials,

respectively, under the competing driving forces of mutual Coulomb attraction and

built-in electric field, and (4) electron-hole recombination at the DA interface. The

whole device structure is divided into simple cubic lattices. We assume uniform light

absorption throughout the junction.


Charge-transfer leads to GEHP separated at an initial distance, with the electron

residing in the acceptor material and the hole in the donor material [1, 5]. We

assume here that the initial GEHP separation dipole vector rinit is randomly oriented

with respect to the local DA interface with a half-space isotropic probability

distribution. The hopping of the electron and hole in the simple cubic lattice is

described using the Miller-Abrahams hopping model [8]:

exp 0

0

ij i

B i

j i

E E

k TRate

E

=


When an electron and hole attempt to occupy the same site, Prec < 1

determines the fraction of those attempts that lead to a recombination event. When

the attempt fails, the hop is canceled such that the system remains unchanged. For

disordered BHJ structure, Prec = 0.1, and e = h = 10-5cm2/Vs, the average

recombination time is 140 ns under open circuit conditions, falling within the range

of experimental observations [9]. We note that our approach does not model non-

geminate recombination.

The simulation parameters listed in Table 2.1 are chosen to match the

CuPc/PTCBI small molecule system. However, it should be noted that the method

and conclusion developed here are applicable to all disordered BHJs.

Table 2.1 Values of physical parameters implemented in the simulation

Parameter Value

Dilectric constant, r 4.0 [3]

Temperature, T 300 K

Lattice constant, d 1 nm

Energy band gap, Eg,D= Eg,A 1.7 eV [2]

Energy offset, IPD - IPA 0.88 eV[2]

Doping density, NA,D=ND,A 1018 cm-3[2]

Initial separation, rinit 2 nm[5]

Recombination factor, Prec 0.1

Exciton diffusion length, LD,D 10 nm[2]

Exciton diffusion length, LD,A 3 nm[2]


2.4 Comparison with experimental data

For geminate recombination model, the extracted number of charge carrier pairs is

proportional to PD, for a fixed light intensity, hence the IQE is proportional to PD as

well. We have compared the simulated IQE vs. V curves with experimental I vs. V

curves obtained for three CuPc/PTCBI heterojunctions with different interface

geometries, as shown in Figure 2.5. The agreement between simulation and

experiment is obtained for the parameters listed in Table 2.1. The IQE, of disordered

and ordered BHJs is higher than that of planar junctions due to the higher exciton

diffusion efficiency, ED. Charge collection in ordered BHJs is less dependent on

electric field compared to disordered BHJs because the carrier diffusion barriers are

removed.


Figure 2.5 ExperimentalI I~V curves (curves) of three various CuPc/PTCBI

devices fitted by simulation results (open dots). Solid (planar), dashed

(disordered BHJ) and dotted (ordered BHJ) experimental curves are from

Ref. [10], [6] and [11], respectively. The disordered BHJ was fitted using the

4.04 nm branch diameter simulated BHJ. The ordered BHJ data was

simulated using an interpenetrating square pillar geometry with a checker-

board arrangement of 40 nm wide pillars. All three model geometries have

an 80 nm thick active region. The BHJ models assume a BHJ region that is

60 nm thick. For all three curves, mobility ratio = 0.01 is applied. All the BHJ

related terms will be explained in later chapters.


2.5 Bibliography



[2] Peumans, Yakimov,Forrest, "Small molecular weight organic thin-film

photodetectors and solar cells," Journal of Applied Physics, vol. 93, pp. 3693, 2003.

[3] F. Peumans , "Separation of geminate charge-pairs at donor-acceptor

interfaces in disordered solids," Chemical Physics Letters, vol. 398, pp. 27, 2004.

[4] Zerza, "Ultrafast charge transfer in conjugated polymer-fullerene

composites," Synth. Met., vol. 119, pp. 637, 2001.

[5] E. A. Silinsh and V. Capek, Organic Molecular Crystals: Interaction,

Localization, and Transport Phenomena. New York: American Institute of Physics,

1994,

[6] Peumans, Uchida,Forrest, "Efficient bulk heterojunction photovoltaic cells

using small-molecular-weight organic thin films," Nature, vol. 425, pp. 158, 2003.

[7] Onsager, "Initial recombination of ions," Physical Review, vol. 54, pp. 554,

1938.

[8] Wolf, "Current injection from a metal to a disordered hopping system. I.

Monte Carlo simulation," Physical Review.B, Condensed Matter, vol. 59, pp. 7507,

1999.


[9] Montanari, "Transient optical studies of charge recombination dynamics in a

polymer/fullerene composite at room temperature," Appl. Phys. Lett., vol. 81, pp.

3001, 2002.

[10] Peumans, Bulovic,Forrest, "Efficient photon harvesting at high optical

intensities in ultrathin organic double-heterostructure photovoltaic diodes," Applied

Physics Letters, vol. 76, pp. 2650, 2000.

[11] Yang,Shtein, Forrest, "Controlled growth of a molecular bulk heterojunction

photovoltaic cell," Nature Materials, vol. 4, pp. 37, 2005.

Chapter 3

3 Doping in donor acceptor heterojunctions

Bilayer organic solar cells with planar structure has been one of the earliest efficient

small molecular solar cells discovered [1], and has been used not only as test bed for

novel materials, but the prototypes for future advanced structured solar cells, such

as light trapping cells [2], or tandem cells [3]. Understanding the physics of this

simple structured device has been crucial for exploring future opportunities,

therefore in this chapter we continue to focus on this structure. We show that the

intrinsic active layer materials cannot provide sufficient electric field for an efficient

charge separation, immediately after the CT process. Doping is the key element that

provides the required electric field, and the existence of doping is proven by

theoretical analysis and experimental verification.

3.1 Electric field insufficiency by intrinsic material

Traditionally, organic materials have been assumed to be undoped, for OPV

applications, at least in experiments where there is no intentional doping step in the

fabrication process. The band diagram for a typical Bilayer cell is shown in Figure 3.1,

where the generation of GEHP and removal of electron and hole is also shown. A

Chapter 3. Doping in donor acceptor heterojunctions 23

typical DA cells with 0.5V built-in voltage and 50nm thickness, will provided 105V/cm

field, uniformly distributed across the whole junction.

Figure 3.1 Band diagram and photocurrent generation in intrinsic bilayer

DA heterojunctions.

We know the organic materials are typically equipped with low dielectric

constant, ~4.0 [4], the Coulomb well is effectively trapping the GEHPs, with a radius around 12nm. This can be seen when equating the Coulomb potential with

thermal energy kT at room temperature. Therefore naturally have the question,

whether the driving force of the built-in electric field is high enough for charge

removal. With Onsagers dissociation model, we can calculate the dissociation of

GEHP with respect to applied electric field, as shown in Figure 3.2, bottom curve. If

we pick a point on this curve where field equals the 105V/cm, which corresponds to


the cells of intrinsic materials, we can see that PD is around 10%, this is far below the

experimental observations.

Figure 3.2 Theoretical result for GEHP dissociation probability vs applied

field, in bilayer cells, top curve. Onsager model is plotted in the bottom

curve, for comparison purpose only.

We know that part of the reason is due to the lack of diffusion barrier in the

model, which enhances the recombination near the interface. With the Monte Carlo

model set up in the previous chapter, we can plot dissociation of GEHP with respect

to applied electric field, as shown in Figure 3.2, the top curve. Obviously, the 105V/cm

field point only provides 30% PD, which is still far below experimental observations.


Now that the diffusion barrier is included, and we know the model has been verified

with experimental results as in previous chapter showed, the only factor that can go

wrong in the analysis procedure is the value of the field. In a word, the field profile in

the device cannot be uniform, and it must be higher in value.

Figure 3.3 Comparison of the band diagram of intrinsic material vs. that of

doped materials, with field across the interface calculated for typical

doping conditions

3.2 Doping enhanced electric field

We know doping can provide concentration of electric field, as shown in Figure

3.3, where in the left figure, we repeated the traditional view, and in the right figure,

we plotted the calculated band diagram of a highly doped pair of materials

combination (1.0e18/cm3). With the high doping concentration, band bending is

allowed to occur in the few layers immediately near the DA interface due to


depletion, and hence field is concentrated heavily into the near interface region. Now

if we look back into Figure 3.2, we see that 106V/cm field gives a PD = 90%, which

exactly matches experimental observations.

3.2.1 Unintentional doping in organic materials

In our previous work, unintentional doping has been revealed to exist in CuPc,

and N,N-bis(2-phenylethyl)-perylene-3,4,9,10-tetracarbonicacid-diimide (BPE-PTCDI)

[5]. In the work, we discovered that unpurified BPE-PTCDI gives a better cell

performance, compared with the control group made with purified material. Purified

material has less impurities, therefore less recombination, and mobility is supposed

to be higher within the device. All these simple facts contradict with this experiment

result. The other interesting behavior of the device is that the performance degrades

much, to comparable fill factor (FF) in around 4 hours of air exposure. The two facts

point to a single clue, there is unintentional n-type doping in the acceptor material,

BPE-PTCDI, and purification and air exposure both remove the dopants. By

capacitance-voltage (CV) measurement, we verified that in a freshly made device

with unpurified material, the doping density is quite high, around 1.2e18/cm3, and

with four hour exposure, the doping levels drops dramatically, to around 1.0e13/cm3.


Figure 3.4 Left: Experimental I~V curve of CuPc/BPE-PTCDI(unpurified),

(squares) freshly made, (triangles) four hour air exposure. Lines are fittings

with model in the work. Right: Short-circuit condition band-diagram with

doping level indicated.

We can then calculated the band diagram, and plot them in Figure 3.4 (right).

We can see that in short circuit condition, the field of the doped group is significantly

higher compared to the dedoped one. Intuitively, steeper field profile gives larger

driving force to separate the charges, hence photocurrent should be higher for this

cell, and vice versa. And this is exactly what we observe experimentally, as shown in

Figure 3.4 left. In order to further verify this argument, we plug the field profile back

into the Monte Carlo model, as we discussed in the previous chapter. The result is a

photocurrent~voltage curve, where shows great fit with experimental results.


3.2.2 Example of organic dopants

As we talked about organic unintentional doping, here is one example of organic

dopant tetrafluorotetracyanoquinodimethane (F4-TCNQ)[6], p-type, shown in Figure

3.5.

Figure 3.5 Doping mechanism of F4-TCNQ as n-type dopant for zinc

phthalocyanine (ZnPc) and N,N-diphenyl-N,N-bis(1-naphthyl)-1,1-

biphenyl-4,4-diamine (-NPD). Figure taken from Ref [6].

The LUMO level of F4-TCNQ is quite close to HOMO level of the matrix material,

for example, ZnPc. And since the concentration of the matrix material is at least two

orders or magnitude larger than the dopants, the LUMO of F4-TCNQ is essentially

filled with electrons coming from HOMO of ZnPc, and the result is the matrix material

is p-type doped.

Doping of -NPD is similar, although in this case HOMO of the matrix material is

slightly lower than the LUMO of the dopant. However due to the overwhelming


population of the HOMO levels, and the size of the energy gap is comparable to kT,

the doping is still efficient.

3.2.3 Capacitance voltage measurement

As we have discussed in the previous sections, capacitance voltage (CV)

measurement is used to get the doping concentration from the devices, and here we

give a brief background introduction on the technique. CV is a very standard

technique used in inorganic p-n junctions, and the principle is based on electrostatics,

which has nothing special at all for inorganics. The expression for doping density

extraction is [7]:

1 = 2 (3.1)

where C is capacitance, A is the area of the device, and VA is the applied voltage. Neff

is effective doping density, defined as:

= + (3.2) where NA and ND are the doping density for donor and acceptor layer of the DA

heterojunction, respectively.

We can see that 1/C2 has a linear relationship with applied voltage, and this is

the method that can be used for experimental data fitting, with the fitted slope

related to effective doping density NB.


3.3 Temperature dependent ionization

We have shown that doping is critical in providing necessary electric field across the

interface for efficient charge separation, by combining controlled doping/dedoping

and IV, CV character analysis. In this section, we are going to carry the analysis one

step further, by measuring the device characteristics in various temperatures.

We know that ionization of dopant molecules is temperature dependent, and if

dopants do exist in active layers of DA junctions, then by varying temperature and

scan the IV and CV characteristics, different behavior should be observed.

3.3.1 Experiment details

We prepared bilayer devices using CuPc as the donor and PTCBI as the acceptor,

using vacuum deposition at


characteristics under illumination are shown in Figure 3.6. Two phenomena draw our

attention. First, the photocurrent in reverse bias (e.g. at -0.5 V) decreases as

temperature decreases. Second, the fill factor degrades strongly as temperature

decreases.

Figure 3.6 Photocurrent vs voltage, for four different temperatures.

ITO/40nm CuPc/40nm PTCBI/100nmAg. Same cell, with all conditions kept

the same, except the temperature.


3.3.2 Temperature dependent exciton diffusion

A CuPc/PTCBI bilayer device biased at a negative voltage is thought to deliver all

electrons and holes generated at the D/A interface to the cathode and anode,

respectively. The change in photocurrent under reverse bias as a function of

temperature is therefore attributed to a change in the number of GEHP generated at

the interface, hence proportional to exciton diffusion efficiency ( ED ) as a function of

temperature. Exciton transport has been studied extensively [4] and can be described

using a hopping model [8] in which the exciton energy at different molecular sites

follows a Gaussian distribution. This results in thermally activated exciton hopping

and an exciton diffusivity (D) of the form:

0 expDED D

k T

= (3.3)

where D0 is a constant, ED is the activation energy that is associated with exciton

hopping, k is Boltzmann constant, and T is the temperature. We know that non-

radiative decay rate is also exponentially related to temperature [4], hence the

exciton diffusion length LD can be expressed as:

= = (3.4)

where C is the combined constant, Eeff is the effective activation energy combining

the diffusivity and lifetime dependency on temperature.


Plugging the exciton diffusion length, LD, into the exciton continuity equation

allows one to calculate the fraction of excitons that reach the DA interface (i.e. the

exciton diffusion efficiency, ED). The continuity equation is:

( )( )( )

2

2

0

0

0 0

0

d p pD G

dx

L D

p x

p x d

G x G

+ =

= = = = = =

(3.5)

where G is the generation source of excitons, by absorption of light, d is the thickness

of donor or acceptor region, and p is the density of excitons. Here, several

assumptions were made. First, light is assumed to be absorbed uniformly within the

80 nm-thick active layer. Second, the donor and acceptor materials are assumed to

have identical activation energy. Third, the D/A interface, cathode and anode all

serve as perfect exciton quenchers. The solution to the above continuity equation is:

( )( )

1 exp /

1 exp /DD

ED

D

d LL

d d L

= +

(3.6)

The dependency of ED on temperature, T, is shown in Figure 3.7(b), where the

measured data points are fitted with calculated curve. The effective activation energy

for the theoretical fit is Eeff = 80 meV, comparable to previously observed exciton


hopping activation energies for organic solids [8]. The corresponding LD is shown in

Figure 3.7(a). At room temperature, LD = 9.3 nm, in agreement with the literature [9].

Figure 3.7 (a) LD as a function of temperature, as calculated with Eeff =

80meV. (b) Experimental photocurrent measured at -1V, scaled by a single

factor (open circles), fitted by calculated exciton diffusion efficiency, with

same parameters as in (a).

3.3.3 Temperature activated ionization

The second observation is that the fill factor decreases as temperature is decreased.

Substantial reverse bias is required to extract all charge carriers at low temperatures.


Figure 3.8 Capacitance voltage measurement, plotted as 1/C2 vs Voltage,

for 200K, 250K, 300K, respectively. Open triangle: experimental data.

Dotted line: theoretical fittings.

In previous sections, we showed that electrical doping plays an important role in

bilayer DA solar cells by providing a strong electric field at the DA interface to

separate geminate pairs. Lowering the temperature will have two effects. First, free

carriers may freeze out on the dopants, lowering the effective doping concentration

and decreasing the electric field. Second, the separation of geminate electron-hole

pairs against their mutual Coulomb attraction is a thermally activated process whose

likelihood decreases as temperature decreases.


Figure 3.9 Solid cureves: Ionization for 4x1017/cm3 doping, 0.27eV doping level, measured from the corresponding LUMO/HOMO. Squares:

experimentally measured ionization level. Plus sign: measured ionization

from the calculated curve. The insets are schematics of the ionization of

dopants

To probe this process, CV measurement were performed at various

temperatures to extract the effective doping density. In Figure 3.8, 1/C2 is plotted as

a function of voltage, for 200K, 250K and 300K. The slope of 1/C2 is a measure of the

effective doping density, Neff. The fitting of the experimental data to theoretical

straight line is shown in dotted lines. We note that symmetric doping was assumed.

The extracted effective doping concentration is plotted as a function temperature in

Figure 3.9. As expected, the effective doping concentration, Neff, decreases as


temperature decreases due to carrier freeze-out. The observed Neff vs T dependence

is consistent with a doping concentration of 4x1017cm-3 and a dopant energy level

0.27eV away from the band edge.

Now we know the free carrier concentration for 200K, 250K and 300K, and we

can pick up a new density value for 150K, for which temperature the measurement of

a CV curve is noisy and unusable. Once we know all the four densities values, this

information can be used to calculate band diagrams as a function of electrical bias

and temperature [5]. Band diagrams under short circuit conditions are shown for

T=300K, 250K, 200K and 150K, in Figure 3.10.


Figure 3.10 Calculated band structure under short circuit condition, for (a) 300K, (b) 250K, (c) 200K, (d) 150K, with ionization values shown in figure 3

(b). Solid lines are LUMO and HOMO levels, dotted lines are Fermi levels.

At 300K, free carrier density is quite high, around 2.8e17/cm3, and it caused

strong band bending near the interface, which translate into strong field, for efficient

GEHP charge separation. Therefore the photocurrent remains high even at applied

voltages close to open circuit voltage, where energy band difference across the

whole junction is almost flat, hence the high fill factor of the photocurrent vs. voltage

characteristic.


However, as temperature lowed, all the way through 150K, ionization of dopants

is stopped, and free carrier concentration dramatically reduced, by one order of

magnitude. This directly translates into very flat band structure, and the field near

the interface is quite weak. The consequence is that high applied voltage is required

to setup the necessary electric field within the junction for efficiency GEHP

separation. At voltages near open circuit voltage, this condition is not met, hence the

photocurrent is much smaller, and the fill factor is much smaller as well. The effect of

carrier freeze-out at low temperatures results in a decrease in electric field at the DA

interface.

Table 3.1 Values of physical parameters implemented in the simulation

Parameter Value

Dilectric constant, r 4.0 [10]

Temperature, T 300K; 250K; 200K; 150K

Lattice constant, d 1 nm

Energy band gap, Eg,D= Eg,A 1.7 eV [9]

Energy offset, IPD - IPA 0.88 eV[9]

Doping density, NA,D=ND,A 1018 cm-3[9]

Initial separation, rinit 2 nm[11]

Recombination factor, Prec 0.1

Exciton diffusion length, LD,D 10 nm[9]

Exciton diffusion length, LD,A 3 nm[9]

Using the value of the electric field at the DA interface as a function of

temperature, the separation efficiency of geminate pairs can be modeled using the

Monte Carlo approach as we discussed in the previous chapter. Parameters are listed

in Table 3.1. The results of these simulations are compared with the measured


photocurrent in Figure 3.11. The result is quite clear here that lowering the

temperature does have a quite strong effect in the photocurrent, and the essential

reason resides in the strong field provided by dopants at higher temperatures.

Figure 3.11 Solid curves: Photocurrent vs voltage, for four different

temperatures. ITO/40nm CuPc/40nm PTCBI/100nmAg. Same cell, with all

conditions kept the same, except the temperature. Open squares:

simulated photocurrent.

3.4 Temperature impact on geminate separation

There are two factors that could affect the GEHP separation, one of which is stated in

the previous section, the dependence of ionization on temperature, the other is


more subtle, the direct impact of thermal energy on the hopping process of electrons

and holes, during the escape of the Coulomb well.

3.4.1 Langiven Capture Radius

More intuitively, as we stated before, the transport mechanism within organic

disordered solids is hopping. After initial separation step, electrons and holes hop

into either of the two consequences: recombine at the interface, or reach the

electrode. There are two competing driving forces for each particle, the Coulomb

attraction and the built-in electric which drives them away, with the former

dominant when the physical distance between the two particles are less than a

threshold distance away from each other. The threshold radius is called Langiven

capture radius[4], rc, the value is roughly equal to the distance where thermal energy

kT balances with Coulomb potential of the oppositely charged particle. Hence the

value increases as temperature decreases, and it becomes increasing harder for the

charges to escape.

3.4.2 Isolating the ionization effect

In order to see which impact, Langiven capture or doping ionization, dominates the

temperature dependent IV characteristics, we performed simulations with fixed

doping profile, and see how Langiven capture changes the IV shape at lowered

temperatures. The results are shown in Figure 3.12. Remember in this set of

simulations, the ionization profile is fixed constant, therefore the impact of field


change is eliminated, and the whole change is due to Langevin captures sensitivity to

temperature. We notice that the temperature range is huge for this set of

simulations, ranging from 200K all the way up to 600K. Clearly, the change is minimal,

with a very flat curve crossing the short circuit condition, indicating the impact of

Langiven capture is very small, for reasonable temperature range, say 200K to 300K.

The conclusion is that in lower temperature range, the whole IV characteristic change,

especially the fill factor and slope change at around short circuit condition, is totally

due to ionization driven field change.

Figure 3.12 IQE vs. voltage, simulated with geminate separation model, with

ionization profile fixed for all temperatures.


3.5 Bibliography

[1] TANG, "2-LAYER ORGANIC PHOTOVOLTAIC CELL," Appl. Phys. Lett., vol. 48, pp.

183, 1986.

[2] Rim, "An effective light trapping configuration for thin-film solar cells," Appl. Phys.

Lett., vol. 91, pp. 243501, 2007.

[3] Ameri and , "Organic tandem solar cells: A review," Energy Environmental Science,

vol. 2, pp. 347, 2009.



[5] Liu, Zhao, Rim, Wu, Konemann,Erk, Peumans, "Control of electric field strength

and orientation at the donor-acceptor interface in organic solar cells," Advanced

Materials, vol. 20, pp. 1065, 2008.

[6] W. Gao, "Electrical doping: The impact on interfaces of $pi@-conjugated

molecular films," Journal of Physics.Condensed Matter, vol. 15, pp. S2757, 2003.

[7] R. F. Pierret, Semiconductor Device Fundamentals. Addison-Wesley Publishing

Company, Inc., 1996,

[8] Schuppel, "Time-resolved luminescence quenching in thin films of perylene-

tetracarboxylic-dianhydride," J Lumin, vol. 110, pp. 309, 2004.

[9] Peumans, Yakimov,Forrest, "Small molecular weight organic thin-film

photodetectors and solar cells," Journal of Applied Physics, vol. 93, pp. 3693, 2003.


[10] F. Peumans , "Separation of geminate charge-pairs at donor-acceptor interfaces

in disordered solids," Chemical Physics Letters, vol. 398, pp. 27, 2004.

[11] E. A. Silinsh and V. Capek, Organic Molecular Crystals: Interaction, Localization,

and Transport Phenomena. New York: American Institute of Physics, 1994,

Chapter 4

4 Geminate separation in bulk

heterojunctions

Planar DA cells, being the earliest efficient small molecular solar cells, have drawn

many research attentions. However, the structure has some inherent flaw, to achieve

high efficiencies. In this chapter, we discuss one of the most successive remedies

tackling this issue, the bulkheterojunction (BHJ) structure. Comparison of different

geometries is presented, followed by their impact on the cell performances.

4.1 Motivation for BHJs

A typical bilayer DA cell is shown in Figure 4.1, with light absorption length and

exciton collection region thickness marked. For efficient photon harvesting, a

thickness more than 100nm is typically required [1]. This number is quite small

already, compared with silicon for visible light absorption (1~10 micrometers),

however, another key parameter critical for photon-electron energy conversion, the

exciton diffusion length LD, is an order of magnitude smaller. LD is unique for organic

material, due to the large binding energy. This means that in a bilayer cell, most of

the photon absorbed contributes to non-radiatively decayed excitons, not

Chapter 4. Geminate separation in bulk heterojunctions 46

photocurrent in the outside circuit. Although we can engineer the electric-magnetic

field within the device by interference and dielectric coating, the return is limited.

Figure 4.1 Bilayer DA photovoltaic cell structure. Light absorption length

and exciton collection region thickness are shown. Exciton collection region

is marked with yellow band.

4.1.1 Bulk heterojunctions

There are multiple ways to overcome this issue, and in Figure 4.2 three methods are

listed, with pioneer work in each field referenced. BHJ appeared in 1995 starting with

polymer materials with solution processing [2, 3], and then in 2004 small molecular

BHJ [4] was successfully fabricated. Since then the field has been actively studied,

especially in the polymer society due to the easy access of solution processing, and

recent breakthrough has even integrated BHJ into tandem cells [5]. The idea is quite

simple, since most excitons away from the DA interface by more than one exciton

diffusion length will most likely decay non-radiatively, an inter-penetration network


of the donor and acceptor material into each others territory can help to collect

these excitons, before the decay ever happens. While at the same time, the device

can still be thick enough so that most photons can still be collected. The benefit does

not come for free, since the networks are usually formed in a random fashion, the

charge collection following the charge transfer step faces twisted pathways. More

detailed analysis is shown later in this chapter.

Figure 4.2 The three methods that tackle the trade-off between long

absorption length and short exciton diffusion length. On the right hand side,

from top to bottom, they are BHJ, tandem cell, and light trapping.

The fabrication of these inter-wined network is realized by dissolving two types

of polymers or one polymer with fullerene derivatives in selected solvents, and spin

cast onto the substrates. For small molecular ones, co-evaporation of two species is


performed. For both of above methods, an annealing follow up step is usually

performed.

4.1.2 Tandem cells

The second structure is tandem cell. A couple good examples are Ref [5] and [6]. In

these cells, thin layers of donor and acceptor materials are deposited one after

another onto the substrate, and for each junction, different donor/acceptor material

combination is used. Therefore the combination is quite flexible. The advantage is

that with altering absorbers, the solar spectrum coverage can be maximized, which

directly translate into higher usage of solar energy. The disadvantage includes a few,

with current matching top the list. If the structure in Figure 4.2 is used, then cells

from each junction are stacked together and current output will be capped by that of

the smallest one. Recent work in the group has proposed multi-terminal device,

which draws the current from each layer separately, in order to avoid direct

current/voltage matching for each individual cell. Whatever matching method used,

the cell will become more incident angle sensitive. The other obvious disadvantage is

the fabrication difficulty, since the transparent electrode being inserted in between

the junctions is not a trivial engineering problem at all.

4.1.3 Light trapping cells

Introducing the inter-penetrating pathways makes the charge collection harder, and

to avoid that, while still maximizing photon absorption, another mechanism is used,


which is light trapping. In this mechanism, light is effectively trapped in the cell, or

between cells, so that photon traverse the active layers multiple times before

escaping the whole device, thus the device can be really thin, which is good for

charge collection, but still harvest most photons. The schematic shown in Figure 4.2

utilizes V-shaped geometry for trapping the photons [7].

Although vastly different from the engineering and fabrication point of view, the

tandem and light trapping cells bears the same micro structure of planar cells,

especially for charge collection process. Therefore, the geminate model applied to

planar cells also applies for these two structures. On the other hand, BHJ bears very

different micro structure compared to planar cells, and need special attention. In the

following sections in this chapter, we are going to model the micro structure, and see

how this can affect the overall device performance.

4.2 Simulation of BHJ structure

The structure of the cell is generated with cellular automata method, which

essentially simulates the spinodal decomposition process. Fabrication of the cells

involves two key steps: co-evaporation, and annealing with cell capped. After the co-

evaporation process, donor and acceptor molecules are mixed on molecular level.

The phase separation then starts when the cell is heated, and final morphology is

determined by temperature and duration that were applied.


The simulation process is directed to mimic this exact process. The whole space

is divided into 80 by 80 by 80 simple cubic lattices, and on each individual lattice

point, a donor or acceptor molecule is randomly assigned. Periodic boundary

condition is applied. Temperature is gradually raised to a certain maximum annealing

temperature Tmax, and then lowered gradually back to room temperature. For each

single step, a neighboring pair of different type molecules is picked, and a decision is

made whether or not the position of this pair of molecules is switched, as shown in

Figure 4.3.

Figure 4.3 Schematic of cellular automata method. This is only cross-section

view of the 3-D simulation. (a) Before exchange, (b) after exchange.

We calculate the enthalpy change before and after the change, according to the

following formula:

(4.1)


where E is the enthalpy of the system, N is the number of molecules, EM(i),M(j) is the

interaction energy between molecule M(i) and M(j). And the switch is performed

according to the following probability:

= 1, 0exp , > 0 (4.2)

where E is the change if the change happened hypothetically. Now we can have an

example of a structure thats generated with this method, as shown in Figure 4.4,

where a whole device structure is shown, ITO/CuPc/CuPc:PTCBI/PTCBI/Ag. Clearly we

can see that phase separation happens during the annealing process, which drives

the two different molecular species into two separate zones. Now the diffusion zone

for electron polaron and hole polaron is still well defined, however, the pathway is

much more twisted compared with the planar junctions. In the analysis in following

sections, we are going t

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